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access icon free Robust guaranteed cost consensus for high-order discrete-time multi-agent systems with parameter uncertainties and time-varying delays

The robust guaranteed cost consensus problem of high-order discrete-time linear multi-agent systems (MASs) with parameter uncertainties and time-varying delays is studied, and a linear consensus protocol of it is designed. Norm-bounded uncertainties and polytopic uncertainties are considered. First, the idea of robust guaranteed cost control is introduced into consensus problems for the MASs, where a cost function is defined based on state errors among neighbouring agents and control inputs of all the agents. Second, by constructing suitable Lyapunov functions and using the stability theory of discrete-time linear systems, two sufficient linear matrix inequality conditions are derived to insure that high-order discrete-time linear MASs with the two types of parameter uncertainties and time-varying delays reach robust guaranteed cost consensus. At the same time, two upper bounds of the guaranteed cost function are also given. Third, convergence results are given as final consensus values of the MASs with parameter uncertainties and time-varying delays. Finally, two numerical comparisons are given to illustrate the correctness and availability of the theoretical results.

References

    1. 1)
      • 17. Guan, Z., Hu, B., Chi, M., et al: ‘Guaranteed performance consensus in second-order multi-agent systems with hybrid impulsive control’, Automatica, 2014, 50, pp. 24152418.
    2. 2)
      • 14. He, W., Cao, J.: ‘Consensus control for high order multi-agent systems’, IET Control Theory Appl., 2011, 5, (1), pp. 231238.
    3. 3)
      • 32. Zhang, G., Xu, J., Zeng, J., et al: ‘Consensus of high-order discrete-time linear networked multi-agent systems with switching topology and time delays’, Trans. Inst. Meas. Control, 2016, pp. 113.
    4. 4)
      • 26. Chesi, G.: ‘On the non-conservatism of a novel LMI relaxation for robust analysis of polytopic systems’, Automatica, 2008, 44, (11), pp. 29732976.
    5. 5)
      • 5. Kar, S., Moura, J.M.F.: ‘Distributed consensus algorithms in sensor networks with imperfect communication: link failures and channel noise’, IEEE Trans. Signal Proc., 2009, 57, (1), pp. 355369.
    6. 6)
      • 28. Wu, M., He, Y., She, J.H., et al: ‘Delay-dependent criteria f or robust stability of time-varying delay systems’, Automatica, 2004, 40, pp. 14351439.
    7. 7)
      • 15. Xin, Y., Cheng, Z.: ‘r-consensus control for discrete-time high-order multi-agent systems’, IET Control Theory Appl., 2013, 7, (17), pp. 21032109.
    8. 8)
      • 29. Wang, Y., Xie, L., Souza de, C.E.: ‘Robust control of a class of uncertain nonlinear systems’, Syst. Control Lett., 1992, 19, (3), pp. 139149.
    9. 9)
      • 19. Wang, Z., Xi, J., Yao, Z., et al: ‘Guaranteed cost consensus problems for second-order multi-agent systems’, IET Control Theory Appl., 2015, 9, (3), pp. 367373.
    10. 10)
      • 16. Xin, Y., Cheng, Z.: ‘r-consensus control for high-order multi-agent systems with digraph’, Asian J. Control , 2013, 15, (5), pp. 15241530.
    11. 11)
      • 22. Xu, J., Zhang, G., Zeng, J., et al: ‘Robust guaranteed cost consensus for high-order discrete-time multi-agent systems with directed graphs’. Proc. The 35th Chinese Control Conf., 2016, pp. 75387545.
    12. 12)
      • 18. Wang, Z., Xi, J., Yao, Z., et al: ‘Guaranteed cost consensus for multi-agent systems with fixed topologies’, Asian J. Control , 2015, 17, (2), pp. 729735.
    13. 13)
      • 20. Cheng, Y., Ugrinovskii, V.: ‘Guaranteed performance leader-follower control for multiagent systems with linear IQC-constrained coupling’. Proc. American Control Conf., 2013, pp. 26252630.
    14. 14)
      • 7. Olfati-Saber, R., Murray, R.M.: ‘Consensus problems in networks of agents with switching topology and time-delays’, IEEE Trans. Autom. Control, 2004, 49, (9), pp. 15201533.
    15. 15)
      • 9. Xi, J., Cai, N., Zhong, Y.: ‘Consensus problems for high-order linear time-invariant swarm systems’, Physica A, 2010, 389, (24), pp. 56195627.
    16. 16)
      • 10. Xi, J., Shi, Z., Zhong, Y.: ‘Output consensus analysis and design for high-order linear swarm systems: partial stability method’, Automatica, 2012, 48, (5), pp. 23352343.
    17. 17)
      • 3. Abdessameud, A., Tayebi, A.: ‘Formation control of VTOL unmanned aerial vehicles with communication delays’, Automatica, 2011, 47, (11), pp. 23832394.
    18. 18)
      • 25. Chesi, G., Garulli, A., Tesi, A., et al: ‘Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: an LMI approach’, IEEE Trans. Autom. Control, 2005, 50, (3), pp. 365370.
    19. 19)
      • 12. Su, Y., Huang, J.: ‘Two consensus problems for discrete-time multi-agent systems with switching network topology’, Automatica, 2012, 48, (9), pp. 19881997.
    20. 20)
      • 31. El Ghaoui, L., Oustry, F., AitRami, M.: ‘A cone complementarity linearization algorithm for static output-feedback and related problems’, IEEE Trans. Autom. Control, 1997, 42, (8), pp. 11711176.
    21. 21)
      • 21. Xie, C.H., Yang, G.H.: ‘Cooperative guaranteed cost fault-tolerant control for multi-agent systems with time-varying actuator faults’, Neurocomputing, 2016.
    22. 22)
      • 27. Fax, J.A., Murray, R.M.: ‘Information flow and cooperative control of vehicle formations’, IEEE Trans. Autom. Control, 2004, 49, (9), pp. 14651476.
    23. 23)
      • 4. Wang, J., Xin, M.: ‘Integrated optimal formation control of multiple unmanned aerial vehicles’, IEEE Trans. Control Syst. Tech., 2013, 21, (5), pp. 17311744.
    24. 24)
      • 33. Horn, R.A., Johnson, C.R.: ‘Matrix analysis’ (Cambridge University Press, 1999).
    25. 25)
      • 24. Ian Petersen, R., Tempo, R.: ‘Robust control of uncertain systems: classical results and recent developments’, Automatica, 2014, 50, (2), pp. 13151335.
    26. 26)
      • 11. You, K., Xie, L.: ‘Network topology and communication data rate for consensusability of discrete-time multi-agent systems’, IEEE Trans. Autom. Control, 2011, 56, (10), pp. 22622275.
    27. 27)
      • 23. Terra, H., Cerri, P., Ishihara, Y.: ‘Optimal robust linear quadratic regulator for systems subject to uncertainties’, IEEE Trans. Autom. Control, 2014, 59, (9), pp. 25862591.
    28. 28)
      • 1. Kang, W., Yeh, H.H.: ‘Coordinated attitude control of multi-satellite systems’, Int. J. Robust Nonlinear Control, 2002, 12, (2), pp. 185205.
    29. 29)
      • 8. Xiao, F., Wang, L.: ‘Consensus problems for high-dimensional multi-agent systems’, IET Control Theory Appl., 2007, 1, (3), pp. 830837.
    30. 30)
      • 13. Zhao, H., Park, J., Zhang, Y., et al: ‘Distributed output feedback consensus of discrete-time multi-agent systems’, Neurocomputing, 2014, 138, (9), pp. 8691.
    31. 31)
      • 2. Godard, K.D., Kumar, K.D.: ‘Fault tolerant reconfigurable satellite formations using adaptive variable structure techniques’, J. Guid. Control Dyn., 2010, 33, (3), pp. 969984.
    32. 32)
      • 30. Ghaoui, L., Feron, E., Balakrishnan, V.: ‘Linear matrix inequalities in system and control theory’ (Society for Industrial and Applied Mathematics, Philadelphia, 1994).
    33. 33)
      • 6. Kibangou, A.Y.: ‘Step-size sequence design for finite-time average consensus in secure wireless sensor networks’, Syst. Control Lett., 2014, 67, (7), pp. 1923.
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